The request may be canceled by http_body, thus allow that when testing.

pkg/http_server/lib/src/http_body_impl.dart

 // Copyright (c) 2013, the Dart project authors.  Please see the AUTHORS file
 // for details. All rights reserved. Use of this source code is governed by a
 // BSD-style license that can be found in the LICENSE file.
 
 part of http_server;
 
 class _HttpBodyHandlerTransformer
     implements StreamTransformer<HttpRequest, HttpRequestBody> {
   final Encoding _defaultEncoding;
 
   const _HttpBodyHandlerTransformer(this._defaultEncoding);
 
   Stream<HttpRequestBody> bind(Stream<HttpRequest> stream) {
     return new Stream<HttpRequestBody>.eventTransformed(
         stream,
         (EventSink<HttpRequestBody> sink) =>
             new _HttpBodyHandlerTransformerSink(_defaultEncoding, sink));
   }
 }
 
 class _HttpBodyHandlerTransformerSink implements EventSink<HttpRequest> {
   final Encoding _defaultEncoding;
   final EventSink<HttpRequestBody> _outSink;
+  int _pending = 0;
+  bool _closed = false;
 
   _HttpBodyHandlerTransformerSink(this._defaultEncoding, this._outSink);
 
   void add(HttpRequest request) {
+    _pending++;
     _HttpBodyHandler.processRequest(request, _defaultEncoding)
-        .then(_outSink.add, onError: _outSink.addError);
+        .then(_outSink.add, onError: _outSink.addError)
+        .whenComplete(() {
+          _pending--;
+          if (_closed && _pending == 0) _outSink.close();
+        });
   }
   void addError(Object error, [StackTrace stackTrace]) {
     _outSink.addError(error, stackTrace);
   }
-  void close() => _outSink.close();
+  void close() {
+    _closed = true;
+    if (_pending == 0) _outSink.close();
+  }
 }
 
 class _HttpBodyHandler {
   static Future<HttpRequestBody> processRequest(
       HttpRequest request,
       Encoding defaultEncoding) {
     return process(request, request.headers, defaultEncoding)
         .then((body) => new _HttpRequestBody(request, body),
               onError: (error) {
                 // Try to send BAD_REQUEST response.
                 request.response.statusCode = HttpStatus.BAD_REQUEST;
                 request.response.close();
-                request.response.done.catchError((_) {});
                 throw error;
               });
   }
 
   static Future<HttpClientResponseBody> processResponse(
       HttpClientResponse response,
       Encoding defaultEncoding) {
     return process(response, response.headers, defaultEncoding)
         .then((body) => new _HttpClientResponseBody(response, body));
   }
@@ skipping 129 matching lines @@
       : super(body.type, body.body);
 }
 
 class _HttpClientResponseBody
     extends _HttpBody implements HttpClientResponseBody {
   final HttpClientResponse response;
 
   _HttpClientResponseBody(this.response, HttpBody body)
       : super(body.type, body.body);
 }